Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO2 reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO2 reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.